In
mathematics, especially in
set theory, when dealing with sets of infinite size, the term
almost or
nearly is used to mean
all the elements except for finitely many.
In other words, an infinite set S that is a subset of another infinite set L, is almost L if the subtracted set L\S is of finite size.
This is conceptually similar to the Almost everywhere concept of Measure theory.
Examples:
- The set <math> S = \{ n \in \mathbf{N} | n \ge k \} </math> is almost N for any k in N, because only finitely many natural numbers are less than k.
- The set of prime numbers is not almost N because there are infinitely many natural numbers that are not prime numbers.